{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2c7f8e43",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1f19aa85",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:18.134850Z",
     "start_time": "2021-10-13T17:12:17.901077Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# 设置随机种子\n",
    "np.random.seed(42)\n",
    "\n",
    "# matplotlib基本设置\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "plt.rcParams['font.sans-serif'] = ['Arial Unicode MS']  # 避免中文乱码\n",
    "# 保存图片的路径\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "# tight_layout=True自动调整子图参数，使之填充整个图像区域,保存图片的函数\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"保存图片:\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7f779235",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-04T14:38:43.574114Z",
     "start_time": "2021-11-04T14:38:43.485075Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 生成随机数据(线性加一个高斯噪声)\n",
    "import numpy as np\n",
    "# 总共一百个自变量\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "429e85c1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-04T14:38:48.225536Z",
     "start_time": "2021-11-04T14:38:48.200704Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.97466943],\n",
       "       [1.25060288],\n",
       "       [0.99153695],\n",
       "       [1.48583462],\n",
       "       [0.4420248 ],\n",
       "       [0.93453225],\n",
       "       [0.07435208],\n",
       "       [1.42289421],\n",
       "       [0.80640538],\n",
       "       [1.75574424],\n",
       "       [1.92108234],\n",
       "       [1.54143656],\n",
       "       [1.97108218],\n",
       "       [1.44123875],\n",
       "       [1.06086523],\n",
       "       [0.48522051],\n",
       "       [0.40977051],\n",
       "       [1.93475779],\n",
       "       [0.01227798],\n",
       "       [0.52097181],\n",
       "       [1.21309746],\n",
       "       [0.5176036 ],\n",
       "       [1.27939267],\n",
       "       [1.62981564],\n",
       "       [1.26272497],\n",
       "       [1.76350743],\n",
       "       [1.49149983],\n",
       "       [1.07779208],\n",
       "       [0.50760481],\n",
       "       [1.48636825],\n",
       "       [1.7886292 ],\n",
       "       [1.51867644],\n",
       "       [1.42256141],\n",
       "       [0.03246072],\n",
       "       [0.43670122],\n",
       "       [0.06573678],\n",
       "       [1.76869942],\n",
       "       [1.65682227],\n",
       "       [0.6349617 ],\n",
       "       [1.49524642],\n",
       "       [0.09192832],\n",
       "       [0.21342788],\n",
       "       [1.78883579],\n",
       "       [0.64034969],\n",
       "       [0.01177203],\n",
       "       [0.9755102 ],\n",
       "       [0.25105265],\n",
       "       [1.44657141],\n",
       "       [0.13114594],\n",
       "       [0.22105735],\n",
       "       [1.28014432],\n",
       "       [1.6200912 ],\n",
       "       [0.82548658],\n",
       "       [0.29486069],\n",
       "       [1.15819079],\n",
       "       [1.62274835],\n",
       "       [1.4430166 ],\n",
       "       [0.90872732],\n",
       "       [1.74394253],\n",
       "       [1.95304108],\n",
       "       [1.93153104],\n",
       "       [0.59728943],\n",
       "       [0.32917378],\n",
       "       [1.66692379],\n",
       "       [1.10618341],\n",
       "       [1.3187186 ],\n",
       "       [0.04660332],\n",
       "       [0.51578702],\n",
       "       [1.5513444 ],\n",
       "       [1.45005219],\n",
       "       [1.01847967],\n",
       "       [1.8675894 ],\n",
       "       [0.39498725],\n",
       "       [1.30270806],\n",
       "       [0.52885909],\n",
       "       [1.8325323 ],\n",
       "       [1.51787138],\n",
       "       [0.7813967 ],\n",
       "       [1.1914666 ],\n",
       "       [1.92227625],\n",
       "       [0.52933528],\n",
       "       [1.48222779],\n",
       "       [0.02166151],\n",
       "       [0.04967301],\n",
       "       [1.77102549],\n",
       "       [1.62468703],\n",
       "       [0.03366145],\n",
       "       [0.91902683],\n",
       "       [0.3725042 ],\n",
       "       [0.82935433],\n",
       "       [0.83806816],\n",
       "       [1.29505678],\n",
       "       [1.85222275],\n",
       "       [0.57837741],\n",
       "       [1.45513286],\n",
       "       [1.70750031],\n",
       "       [0.40334855],\n",
       "       [0.57138933],\n",
       "       [1.63959743],\n",
       "       [1.44519642]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b8a8e3c9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:05.702979Z",
     "start_time": "2021-10-13T08:02:05.296892Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 线性回归函数\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对随机数据进行绘图\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])  # x轴的范围:[0,2],y轴的范围:[0,15]\n",
    "save_fig(\"线性回归函数\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "517c3e85",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 标准方程(实际上就是正规方法)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "749154fe",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:08.927882Z",
     "start_time": "2021-10-13T08:02:08.919791Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones(X.shape), X]  # 相对于标准方程里面的X\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)  # 正规方程的解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "005a1b3c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:11.321247Z",
     "start_time": "2021-10-13T08:02:11.313615Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best # 求出代价最小的参数值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b142414c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:14.068937Z",
     "start_time": "2021-10-13T08:02:14.061858Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 验证一下数据\n",
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new] \n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0461ac5e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:17.206751Z",
     "start_time": "2021-10-13T08:02:16.927113Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 拟合的线性回归\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘图拟合的图形\n",
    "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"拟合的线性回归\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "72f942e6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:21.147840Z",
     "start_time": "2021-10-13T08:02:20.664899Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 线性回归模型\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()  # 创建线性回归对象\n",
    "lin_reg.fit(X, y)  # 开始训练模型\n",
    "lin_reg.intercept_, lin_reg.coef_  # 得到的特征权值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4832f77b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:23.840675Z",
     "start_time": "2021-10-13T08:02:23.832843Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9065b54",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "LinearRegression是建立在scipy.linalg.lstsq()基础上的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8d2d10e0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:26.630468Z",
     "start_time": "2021-10-13T08:02:26.621032Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.linalg.lstsq()实现线性回归,代表就是最小二乘法\n",
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c124f1e2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:29.501751Z",
     "start_time": "2021-10-13T08:02:29.491535Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 计算一个伪逆,奇异值分解(SVD)   实际上就是标准方程里面的X进行计算伪逆\n",
    "np.linalg.pinv(X_b).dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dacd2628",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 梯度下降"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d946be4",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "梯度下降是一种优化算法,能够为大范围的问题找到一个最优解,梯度下降的中心思想就是迭代地调整参数从而使成本函数最小化"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "478355de",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 批量梯度下降"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f44d5cf",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "编程实现批量梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ee398e1f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:33.971311Z",
     "start_time": "2021-10-13T08:02:33.949063Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eta=0.1 # 学习率\n",
    "n_iterations = 1000  # 需要迭代地次数\n",
    "\n",
    "m=100 # 训练数据数量\n",
    "\n",
    "theta = np.random.randn(2,1)  #随机第一次的特征权值\n",
    "\n",
    "for i in range(n_iterations):\n",
    "    temp=2/m * X_b.T.dot(X_b.dot(theta)-y)    # 成本函数的偏导数\n",
    "    theta=theta-eta*temp   # 下一个的特征权值\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2993ce31",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:38.579027Z",
     "start_time": "2021-10-13T08:02:38.566376Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "theta_path_bgd = []\n",
    "# 绘画一定学习率的梯度下降曲线\n",
    "def plot_gradient_descent(theta, eta,theta_path=None):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")  # 绘制原始图像\n",
    "    n_iterations = 1000\n",
    "    for iteration in range(n_iterations):\n",
    "        # 当剩下最后10迭代的时候开始绘图\n",
    "        if iteration < 10:\n",
    "            y_predict = X_new_b.dot(theta)\n",
    "            style = \"b-\" if iteration > 0 else \"r--\"\n",
    "            plt.plot(X_new, y_predict, style)\n",
    "        gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)  # 求成本函数的偏导数\n",
    "        theta = theta - eta * gradients   # 进行循环迭代\n",
    "        if theta_path is not None:\n",
    "            theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)\n",
    "    #print(\"梯度下降中得到的值是: \",theta_path_bgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ff100fcd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:50.293627Z",
     "start_time": "2021-10-13T08:02:48.588003Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 不同学习率批量梯度下降\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 2160x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # 初始化一个参数\n",
    "\n",
    "plt.figure(figsize=(30,10))\n",
    "# 第一个\n",
    "plt.subplot(131); plot_gradient_descent(theta, eta=0.02);plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "# 第二个\n",
    "plt.subplot(132); plot_gradient_descent(theta, eta=0.1,theta_path=theta_path_bgd)\n",
    "# 第三\n",
    "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
    "# 保存图像\n",
    "save_fig(\"不同学习率批量梯度下降\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdb35c4c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 随机梯度下降(随机可以逃离局部最优)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fe2c00a",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "使用SGD随机梯度下降模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "24760729",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:02:55.963907Z",
     "start_time": "2021-10-13T08:02:55.945631Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(eta0=0.1, penalty=None, random_state=42)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-3, penalty=None, eta0=0.1, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "dee0d1d1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:03:01.614702Z",
     "start_time": "2021-10-13T08:03:01.608013Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.24365286]), array([2.8250878]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 查看特征权值\n",
    "sgd_reg.intercept_,sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "32545e76",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:03:05.135496Z",
     "start_time": "2021-10-13T08:03:05.131332Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X_b)\n",
    "np.random.seed(42)  # 种下随机种子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "73eff676",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:03:08.121254Z",
     "start_time": "2021-10-13T08:03:07.791210Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 随机梯度下降\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50  # 用来改变学习率用的\n",
    "t0, t1 = 5, 50  # 来改变学习率的\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2,1)  # 随机初始化特征权值\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        # 前二十次的迭代\n",
    "        if epoch == 0 and i < 20:                   \n",
    "            y_predict = X_new_b.dot(theta)           \n",
    "            style = \"b-\" if i > 0 else \"r--\"         \n",
    "            plt.plot(X_new, y_predict, style)        \n",
    "        random_index = np.random.randint(m)  # 随机抽取数据\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)   # 成本函数的偏导数\n",
    "        eta = learning_schedule(epoch * m + i)   # 进行改变学习率\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)                 \n",
    "\n",
    "plt.plot(X, y, \"b.\")                                 \n",
    "plt.xlabel(\"$x_1$\", fontsize=18)                     \n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)           \n",
    "plt.axis([0, 2, 0, 15])                             \n",
    "save_fig(\"随机梯度下降\")                                \n",
    "plt.show()                                           "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c58a67",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 小批量梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9fccff5e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:03:12.827902Z",
     "start_time": "2021-10-13T08:03:12.808485Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 小批量梯度下降代码实现\n",
    "theta_path_mgd = []\n",
    "\n",
    "n_iterations = 50   # 需要迭代的次数\n",
    "minibatch_size = 20\n",
    "\n",
    "np.random.seed(42)  # 种下随机种子\n",
    "theta = np.random.randn(2, 1)  # 初始化特征权值\n",
    "\n",
    "t0, t1 = 200, 1000\n",
    "\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "\n",
    "t = 0\n",
    "for epoch in range(n_iterations):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for i in range(0, m, minibatch_size):\n",
    "        t += 1\n",
    "        xi = X_b_shuffled[i:i+minibatch_size]\n",
    "        yi = y_shuffled[i:i+minibatch_size]\n",
    "        gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a29fa3a1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:03:16.623840Z",
     "start_time": "2021-10-13T08:03:16.607454Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 三种梯度下降的特征权值\n",
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a89fa2f2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T08:03:19.113761Z",
     "start_time": "2021-10-13T08:03:18.741558Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 各种梯度下降比较\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 进行可视化展示\n",
    "\n",
    "plt.figure(figsize=(7,4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"批量梯度下降\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"小批量梯度下降\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"随机梯度下降\")\n",
    "plt.legend(loc=\"upper left\", fontsize=16)\n",
    "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
    "plt.ylabel(r\"$\\theta_1$   \", fontsize=20, rotation=0)\n",
    "plt.axis([2.5, 4.5, 2.3, 3.9])\n",
    "save_fig(\"各种梯度下降比较\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6b05a8f",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 多项式回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "baf9d450",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:11:53.484623Z",
     "start_time": "2021-10-13T17:11:53.299999Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ecffb3ba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:14:00.090876Z",
     "start_time": "2021-10-13T17:14:00.083824Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 创建二项式数据ss\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "baa7fe24",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:27.619626Z",
     "start_time": "2021-10-13T17:12:27.224680Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 二项式回归\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 进行可视化二项式回归数据\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"二项式回归\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "37573d56",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:31.122177Z",
     "start_time": "2021-10-13T17:12:30.658930Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# PolynomialFeatures将每个特征的平方看成了一个新特征\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)  # 包含了X的原始数据与X的平方数据\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f06b94ea",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:33.036710Z",
     "start_time": "2021-10-13T17:12:33.028541Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "91cbe5ef",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:35.164279Z",
     "start_time": "2021-10-13T17:12:35.097091Z"
    },
    "collapsed": true,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'LinearRegression' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-b0da87cfd5f7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# 把它视作线性回归\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mlin_reg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mLinearRegression\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mlin_reg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_poly\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mlin_reg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintercept_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlin_reg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoef_\u001b[0m  \u001b[0;31m# 得到跟线性回归类似的权值\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'LinearRegression' is not defined"
     ]
    }
   ],
   "source": [
    "# 把它视作线性回归\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_  # 得到跟线性回归类似的权值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2fb8ba1e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:42.705424Z",
     "start_time": "2021-10-13T17:12:42.681008Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'lin_reg' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-e4ca1944d93f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mX_new\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# 随机X\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mX_new_poly\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpoly_features\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtransform\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_new\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# 转换为俩个特征值输入(X的平方特征,与X)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0my_new\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlin_reg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_new_poly\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"b.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_new\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_new\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"r-\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"预测\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'lin_reg' is not defined"
     ]
    }
   ],
   "source": [
    "X_new=np.linspace(-3, 3, 100).reshape(100, 1)  # 随机X\n",
    "X_new_poly = poly_features.transform(X_new)  # 转换为俩个特征值输入(X的平方特征,与X)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"预测\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"二项式回归拟合\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d98108c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 学习曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0bd73588",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:51.013443Z",
     "start_time": "2021-10-13T17:12:50.985931Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'LinearRegression' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-11-a67f16e58092>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mpolybig_features\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPolynomialFeatures\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdegree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdegree\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minclude_bias\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mstd_scaler\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mStandardScaler\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m     \u001b[0mlin_reg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mLinearRegression\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m     polynomial_regression = Pipeline([\n\u001b[1;32m      9\u001b[0m             \u001b[0;34m(\u001b[0m\u001b[0;34m\"poly_features\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpolybig_features\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'LinearRegression' is not defined"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "            (\"poly_features\", polybig_features),\n",
    "            (\"std_scaler\", std_scaler),\n",
    "            (\"lin_reg\", lin_reg),\n",
    "        ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"线性回归与二项式回归比较\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e67b3d95",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:12:57.558258Z",
     "start_time": "2021-10-13T17:12:57.508960Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error  # 计算均方误差回归损失\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    # 划分训练与测试集,训练:测试=1:5\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []  # 训练集的均分误差,测试集的均分误差\n",
    "    # 在不同的训练子集上进行多次训练模型\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:m], y_train_predict))  # 训练集的均方误差\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))            # 测试集的均方误差\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"训练\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"验证\")\n",
    "    plt.legend(loc=\"upper right\", fontsize=14)    # 设置图例位置\n",
    "    plt.xlabel(\"训练设置的大小\", fontsize=14) \n",
    "    plt.ylabel(\"均方根误差\", fontsize=14)              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c5b1e472",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:09.467638Z",
     "start_time": "2021-10-12T13:21:09.205788Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 线性回归的学习曲线\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "plt.axis([0, 80, 0, 3])                         \n",
    "save_fig(\"线性回归的学习曲线\")   \n",
    "plt.show()   \n",
    "# 从图中我们可以看出训练集在刚开始的是均方误差是0,此时模型能更好拟合数据,随着训练集的增加,模型的均方误差越来越大,此时就无法完全拟合了\n",
    "# 验证集刚开始的时候,它无法正确泛化数据,导致均方误差非常大,随着模型的不断的学习,验证集的均方误差也慢慢下降了,逐渐趋于平稳\n",
    "# 下图属于欠拟合的模型,俩条的均方误差都比较高"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "be382e35",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-13T17:13:04.102476Z",
     "start_time": "2021-10-13T17:13:04.079006Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'LinearRegression' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-c4752d66edf2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m polynomial_regression = Pipeline([\n\u001b[1;32m      4\u001b[0m         \u001b[0;34m(\u001b[0m\u001b[0;34m\"poly_features\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mPolynomialFeatures\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdegree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minclude_bias\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m         \u001b[0;34m(\u001b[0m\u001b[0;34m\"lin_reg\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mLinearRegression\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     ])\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'LinearRegression' is not defined"
     ]
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "# 采用10阶的多项式模型进行训练 ,polynomial_regression类似一个管道一样,按顺序执行\n",
    "polynomial_regression = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=2, include_bias=False)),\n",
    "        (\"lin_reg\", LinearRegression()),\n",
    "    ])\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "plt.axis([0, 80, 0, 3])           \n",
    "save_fig(\"2阶多项式的学习曲线\")  \n",
    "plt.show()        \n",
    "# 从图中我们可以看出均方误差比上要低很多,并且都是趋向平稳,我们称为它为过拟合模型"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c378c11",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 正则化线性模型"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2a335fe",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 岭回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "73409579",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:09.752680Z",
     "start_time": "2021-10-12T13:21:09.749330Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 创建线性回归数据\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "9646674b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:09.759756Z",
     "start_time": "2021-10-12T13:21:09.754751Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55071465]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)   # 采用闭式解的一种岭回归\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c755b403",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:09.765316Z",
     "start_time": "2021-10-12T13:21:09.760774Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5507201]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)   # 采用随机梯度下降的岭回归\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "94595450",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:10.302755Z",
     "start_time": "2021-10-12T13:21:09.766334Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 岭回归\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
    "    for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
    "        model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
    "        if polynomial:\n",
    "            model = Pipeline([\n",
    "                    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "                    (\"std_scaler\", StandardScaler()),\n",
    "                    (\"regul_reg\", model),\n",
    "                ])\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\", fontsize=15)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 3, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "\n",
    "save_fig(\"岭回归\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fa65a1c",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Note**: to be future-proof, we set `max_iter=1000` and `tol=1e-3` because these will be the default values in Scikit-Learn 0.21."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "2f546b69",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:10.308348Z",
     "start_time": "2021-10-12T13:21:10.303798Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.47012588])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\", max_iter=1000, tol=1e-3, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d523d15",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Lasso回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "6d736d11",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:10.786112Z",
     "start_time": "2021-10-12T13:21:10.309371Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/tf2/lib/python3.7/site-packages/sklearn/linear_model/_coordinate_descent.py:532: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 2.802867703827455, tolerance: 0.0009294783355207351\n",
      "  positive)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: Lass回归\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), random_state=42)\n",
    "\n",
    "save_fig(\"Lass回归\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ac299900",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:10.795788Z",
     "start_time": "2021-10-12T13:21:10.787541Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3fbc16cd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:10.814659Z",
     "start_time": "2021-10-12T13:21:10.799705Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.47177422])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用随机梯度下降进行替换\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "sgd_reg=SGDRegressor(penalty=\"l1\")\n",
    "sgd_reg.fit(X,y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "23e829b5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:10.831209Z",
     "start_time": "2021-10-12T13:21:10.821491Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5a519d08",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:10.908975Z",
     "start_time": "2021-10-12T13:21:10.836779Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[1, 1], [1, -1], [1, 0.5]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "66f3a9f6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:12.094525Z",
     "start_time": "2021-10-12T13:21:10.913969Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: Lasso与岭回归的对比\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 727.2x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.05, n_iterations = 200):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + l2 * theta\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10.1, 8))\n",
    "for i, N, l1, l2, title in ((0, N1, 2., 0, \"Lasso\"), (1, N2, 0,  2., \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * 0.5 * N2**2\n",
    "    \n",
    "    tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
    "    levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
    "    levelsN=np.linspace(0, np.max(N), 10)\n",
    "    \n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(np.array([[2.0], [0.5]]), Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
    "\n",
    "    ax = axes[i, 0]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, N / 2., levels=levelsN)\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.set_title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "    ax.set_ylabel(r\"$\\theta_2$\", fontsize=16, rotation=0)\n",
    "\n",
    "    ax = axes[i, 1]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    ax.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.plot(t1r_min, t2r_min, \"rs\")\n",
    "    ax.set_title(title, fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "\n",
    "save_fig(\"Lasso与岭回归的对比\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dbc49ac4",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "2adbeb95",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 弹性网络"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "07247f22",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:12.099153Z",
     "start_time": "2021-10-12T13:21:12.095508Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 介于Lasso回归与岭回归之间,l1_ratio对应r,类似一种偏向的意思\n",
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b3f92ed",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 提前停止(当RMSE到底了最小了,要及时止损)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d175518c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:12.104741Z",
     "start_time": "2021-10-12T13:21:12.100413Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# 创建一个高阶多项式回归数据\n",
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "87ca01bc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:12.468159Z",
     "start_time": "2021-10-12T13:21:12.105880Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "# 对数据集进行预处理\n",
    "poly_scaler = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
    "        (\"std_scaler\", StandardScaler())\n",
    "    ])\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "minimum_val_error = float(\"inf\")  # 最小值\n",
    "best_epoch = None   # 最好模型的迭代次数\n",
    "best_model = None   # 最好模型\n",
    "for epoch in range(1000):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)  # 不断的进行训练,warm_start=True指的是从停止的地方继续训练\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)  # 对验证集进行验证\n",
    "    val_error = mean_squared_error(y_val, y_val_predict)  # 计算RSE\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = deepcopy(sgd_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "aa418175",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:12.940765Z",
     "start_time": "2021-10-12T13:21:12.469204Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 提前停止训练\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    train_errors.append(mean_squared_error(y_train, y_train_predict))\n",
    "    val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "best_epoch = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_val_rmse),\n",
    "             xytext=(best_epoch, best_val_rmse + 1),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "             fontsize=16,\n",
    "            )\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"验证集\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"训练集\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "save_fig(\"提前停止训练\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9d606714",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:12.944983Z",
     "start_time": "2021-10-12T13:21:12.941900Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239,\n",
       " SGDRegressor(eta0=0.0005, learning_rate='constant', max_iter=1, penalty=None,\n",
       "              random_state=42, tol=-inf, warm_start=True))"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_epoch, best_model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d98f3858",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-08T07:12:30.765257Z",
     "start_time": "2021-10-08T07:12:29.801486Z"
    },
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 逻辑回归"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0e413ac",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 估计概率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "4e5b2890",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.385729Z",
     "start_time": "2021-10-12T13:21:12.946143Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 逻辑回归的sigmoid函数\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot([-10, 10], [0, 0], \"k-\")\n",
    "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-10, 10], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\", fontsize=20)\n",
    "plt.axis([-10, 10, -0.1, 1.1])\n",
    "save_fig(\"逻辑回归的sigmoid函数\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd312062",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 训练和成本函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35f870f3",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 决策边界"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "f2ec1750",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.438671Z",
     "start_time": "2021-10-12T13:21:13.390146Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename']"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "debfe638",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.445374Z",
     "start_time": "2021-10-12T13:21:13.440590Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "786be162",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.452463Z",
     "start_time": "2021-10-12T13:21:13.447719Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:]  # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)  # 1 if Iris virginica, else 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d4300de",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "**Note**: To be future-proof we set `solver=\"lbfgs\"` since this will be the default value in Scikit-Learn 0.22."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "489065bc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.472220Z",
     "start_time": "2021-10-12T13:21:13.455877Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(random_state=42)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", random_state=42)\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "0eac3120",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.593466Z",
     "start_time": "2021-10-12T13:21:13.478397Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb228855790>]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris virginica\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5d6ae01",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The figure in the book actually is actually a bit fancier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "50aa815f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.906231Z",
     "start_time": "2021-10-12T13:21:13.595976Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: 鸢尾花的逻辑回归\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/envs/tf2/lib/python3.7/site-packages/matplotlib/patches.py:1338: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  verts = np.dot(coords, M) + (x + dx, y + dy)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris virginica\")\n",
    "plt.text(decision_boundary+0.02, 0.15, \"Decision  boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
    "plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n",
    "plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "save_fig(\"鸢尾花的逻辑回归\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "02540f88",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.909967Z",
     "start_time": "2021-10-12T13:21:13.907249Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.66066066])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "8b0f114d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:13.914630Z",
     "start_time": "2021-10-12T13:21:13.911182Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "5ecf25f9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:14.262327Z",
     "start_time": "2021-10-12T13:21:13.915752Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)\n",
    "\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", C=10**10, random_state=42)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "        np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "087ba8c9",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Softmax回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "cd1387d3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:14.273973Z",
     "start_time": "2021-10-12T13:21:14.263420Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, multi_class='multinomial', random_state=42)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10, random_state=42)\n",
    "softmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "a78c9a98",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:14.684285Z",
     "start_time": "2021-10-12T13:21:14.275027Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "保存图片: softmax_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "5ae10f5d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:14.688140Z",
     "start_time": "2021-10-12T13:21:14.685447Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "27e0dbae",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-10-12T13:21:14.707781Z",
     "start_time": "2021-10-12T13:21:14.689347Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8fc2585",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 练习题"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c0bacddb",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de81967c",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bbf8cd62",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "90aa11a9",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d73dabb",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "846d3a58",
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tf",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.18"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "288px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
